How much discrepency would I get if I used acceleration due to gravity?

[sodium40mg]

How much error would I get if I used 9.8 m/s^2 as the acceleration for a falling object in an experiment? For example, if I have a ball at, say, shoulder's length up in the air and I had someone measure the time it took for the ball to hit the ground. Would I get a lot of error if I used the equation

d = vi * t - 1/2 * a * t^2

Where vi = 0 m/s, so d = -1/2 * a * t^2 and a = - 9.8 m/s^2

Would that actually equal the distance from the shoulder length to the ground or how much error would I get? Would it be significant?

 

[Pengwuino]

Well exactly where are you trying to examine the erorr from? The fact that you're only using 2 significant figures?

 

[uart]

How much error would I get if I used 9.8 m/s^2 as the acceleration for a falling object in an experiment? For example, if I have a ball at, say, shoulder's length up in the air and I had someone measure the time it took for the ball to hit the ground. Would I get a lot of error if I used the equation


Would that actually equal the distance from the shoulder length to the ground or how much error would I get? Would it be significant?

Are you talking about measurement error in the timing?

Or are you talking more fundamentally about the applicability of the equation to the real world problem? The biggest discrepancy in the fundamental equation would be that it ignores air resistance. For a ball dropped from about head height the velocity is fairly low so for in most cases the effect of air resistance would be small, but if the ball was extremely low in mass then air resistance could significantly alter the result. In other words, the formula should be quite accurate for a cricket ball but not necessarily so for a ping pong ball.

 

[uart]

Here's a quick test of whether air resistance will be significant.

Final velocity (ideally) when dropped from 1.8m = 5.9 m/s

Air density at 20C, rho = 1.2 kg/m^2

1. Cricket ball. m = 0.16 kg, frontal area A = 0.0041 m^2, coeff of drag, cd = 0.47.

Air resistance at final velocity, F = 1/2 rho cd A v^2 = 0.041 N

Comparing the above with the force due to gravity of 1.6N we see that the drag is negligible.

2. Pin pong ball. Mass = 0.0027 kg, Frontal area A = 0.00126 m^2, drag coeff cd = 0.47

Air resistance at (ideal) final velocity, F = 1/2 rho cd A v^2 = 0.0125 N.

Comparing the above with the gravitational force of just 0.027 N we see that air resistance would be very significant in this case.